# Tagged Questions

51 views

### Limit of Binomial distribution

In showing us that Binomial distribution: $$B_{N,p}(n) := \binom {N}{n} p^n(1-p)^{N-n}$$ tends to Poisson's: $$P_ \lambda (n) = \dfrac {\lambda ^n}{n!}e^{-\lambda}$$where I guess lambda should be ...
75 views

### Convergent sequences and proof

Prove that $\dfrac{1+n}{n^2}$ converges as $n \to \infty$ How do I go about constructing this proof? Can I use the definition that $\operatorname{abs}(a_n - L < \epsilon)$?
124 views

66 views

### Proving a limit $\lim\limits_{x\to \infty}\frac{x-3}{x^2 +1}$ as $x$ goes to infinity using $\epsilon-\delta$

Hi i need to prove that $$\lim_{x\to \infty}\frac{x-3}{x^2 +1}=0$$ using the formal definition of a limit. Can anyone help?
44 views

### Question regarding a Limit involving Logs.

Suppose $A$ is a positive integer and $\delta>0$. Assume the $(n_i)$ are the denominators of a continued fraction representation of the irrational number $[0,a_1,a_2\ldots],$ where $a_{k+1}=A$ ...
198 views

### Problem of limit with binomial coefficients

I thought that the following would made a nice exercise, but I am not sure how to evaluate its difficulty since I often miss elementary solutions. How about you try answering it? It would be great to ...
117 views

38 views

### Analysis of a limit

I believe I understand this question but I am stuck at what seems to be a "last part." Here is the question: Suppose that the function $f: \mathbb{R} \rightarrow \mathbb{R}$ is differentiable at ...
113 views

### What are common methods/techniques can be used to prove that limit of an infinite sequence exists?

I would like to know what are common methods can be used to show that an infinite sequence converges. From what I know so far, If a sequence is bounded and monotonic increasing/decreasing then it ...
### Proving $\lim_{x \to \infty} \sqrt{1+4x+x^{2}}-x=2$ [duplicate]
Possible Duplicate: Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt$n${x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$ Consider the limit $$\lim_{x \to \infty} \sqrt{1+4x+x^{2}}-x$$ ...